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A comment on a conjecture of N. Wiener

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  • Rosenblatt, M.

Abstract

N. Wiener conjectured that a necessary and sufficient condition for a stationary process to be representable as a one-sided function of a sequence of independent, identically distributed random variables and its shifts is that its backward tail field be trivial. Here it is shown that the condition is not sufficient for such a representation.

Suggested Citation

  • Rosenblatt, M., 2009. "A comment on a conjecture of N. Wiener," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 347-348, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:3:p:347-348
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    Cited by:

    1. Richard C. Bradley & Richard A. Davis & Dimitris N. Politis, 2021. "Preface to the Murray Rosenblatt memorial special issue of JTSA," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 495-498, September.
    2. Wu, Wei Biao & Huang, Yinxiao & Huang, Yibi, 2010. "Kernel estimation for time series: An asymptotic theory," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2412-2431, December.
    3. Merlevède, F. & Peligrad, M., 2016. "On the empirical spectral distribution for matrices with long memory and independent rows," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2734-2760.
    4. Laurent, Stéphane, 2010. "Further comments on the representation problem for stationary processes," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 592-596, April.

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